If ${z_r} = \cos \frac{{r\alpha }}{{{n^2}}} + i\sin \frac{{r\alpha }}{{{n^2}}},$ where $r = 1, 2, 3, \dots, n$,then $\mathop {\lim }\limits_{n \to \infty } \,{z_1}{z_2}{z_3}\dots{z_n}$ is equal to

The highest stable $Mn$ fluoride is $MnF_4$,whereas the highest $Mn$ oxide is $Mn_2O_7$. This is due to $-$

If the foci of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ and the hyperbola $\frac{x^2}{4}-\frac{y^2}{b^2}=1$ coincide,then $b^2$ is equal to

The total number of $RNA$ strands in an animal virus is:

Two point masses of $0.3\, kg$ and $0.7\, kg$ are fixed at the ends of a rod of length $1.4\, m$ and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum is located at a distance of

For the reaction $A + B \rightarrow C$,experiments were performed in the presence of a large amount of $B$ to measure the initial reaction rate $(V_f)$ as a function of the initial concentration of $A ([A]_0)$. The data from the experiments are plotted as shown below. The order of the reaction with respect to $A$ is $.....$